We performed molecular dynamics simulations of the hydration of Na+ and K+ in infinitely long single-walled armchair carbon nanotubes (CNTs) at 298 K. Simulation results indicate that the preferential orientation of water molecules in coordination shells of these two cations presents an anomalous change in the CNTs and causes a diameter-dependent variation for the interaction energy between the cation and water molecules in its coordination shell. In the five CNTs of this work, it is energetically favorable for confining a hydrated K+ inside the two narrow CNTs with diameters of 0.60 and 0.73 nm, whereas the situation is reverse inside the wide CNTs with diameters of 0.87, 1.0, and 1.28 nm. This finding is important for CNT applications in ionic systems that control the selectivity and the ionic flow.